Statistics question - area codes?

I am trying to solve the following statistics question:



I am looking for three-digit area codes with 1 or 0 in the second digit. Exclude codes ending in 00 or 11 and codes beginning with 0 or 1. How many area codes are possible under these conditions?



Please help me by explaining, because if you just tell me the answer, I can't learn how to solve it. Actually, I know the answer, but not how to get there.



Thanks in advance for your help.Statistics question - area codes?
you have 8 possible numbers for the first digit, because you can't have 1 or 0



you only have 2 possible numbers for the second digit, because you can only have 0 or 1



you only have 9 possible numbers for the third digit, b/c you can't end in 00 or 11, so if you are using 0 for the second digit, you can use any digit but 0, likewise, if you are using 1 for the second digit, you can use any digit but 1...



therefore,

the answer is



8 x 2 x 9 = 144Statistics question - area codes?
The first digit has 8 possibilities which are 2, 3, 4, 5, 6, 7, 8, 9.



On the second digit, there are 2 kinds of possibilities.



Number 1 - Second digit is 0 or 1, if it's like this the third digit has only 9 possibilities (can't be the same as second digit). For this, there are 8 * 2 * 9 = 144 possibilities.



Number 2 - Second digit is not 0 or 1 so third digit has 10 possibilities (it doesn't matter what number it is). For this there are 8 * 8 * 10 = 640 possibilities.



Therefore there are 640 + 144 = 784 possibilities.

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